How does subtracting a positive constant, k, from an exponential function affect its horizontal asymptote?

Subtracting a positive constant k from a parent exponential function results in the horizontal asymptote shifting down k units.

For example, untranslated, a parent exponential function of the form y = aˣ (a > 0, a≠1) has a horizontal asymptote at y = 0.

y = 2ˣ - 3 has a horizontal asymptote at y = - 3 as we are subtracting 3 from the parent. All values from the original get shifted down 3 units.

y = 7ˣ - 5 has a horizontal asymptote at y = - 5 as we are subtracting 5 from it.

(Conversely, adding a positive constant k results in an upward shift k units. E. g., y = 3ˣ + 2 has a horizontal asymptote at y = 2)